3 Suspended masses A system of masses and springs is shown in the adjacent figure, for which ki = 6 N m', k2- 15 N m', and ks - 78 N m'. Assume that the blocks move vertically with no rotation or side-to-side swinging. a) Show that the normal mode angular frequencies are 2 rad s' and 3 rad s', and find the corresponding normal modes. ki 4 kg k2 The blocks are held in their equilibrium positions; the 4 kg block is then displaced 1 cm upwards and the system is released from rest. b) Find expressions for the subsequent displacements of both blocks. 12 kg ooo0000000
3 Suspended masses A system of masses and springs is shown in the adjacent figure, for which ki = 6 N m', k2- 15 N m', and ks - 78 N m'. Assume that the blocks move vertically with no rotation or side-to-side swinging. a) Show that the normal mode angular frequencies are 2 rad s' and 3 rad s', and find the corresponding normal modes. ki 4 kg k2 The blocks are held in their equilibrium positions; the 4 kg block is then displaced 1 cm upwards and the system is released from rest. b) Find expressions for the subsequent displacements of both blocks. 12 kg ooo0000000
Related questions
Question
Transcribed Image Text:3 Suspended masses
A system of masses and springs is shown in the adjacent figure, for which ki = 6 N m',
k2- 15 N m', and ks - 78 N m'. Assume that the blocks move vertically with no rotation
or side-to-side swinging.
a) Show that the normal mode angular frequencies are 2 rad s' and 3 rad s', and find
the corresponding normal modes.
ki
4 kg
k2
The blocks are held in their equilibrium positions; the 4 kg block is then displaced 1 cm
upwards and the system is released from rest.
b) Find expressions for the subsequent displacements of both blocks.
12 kg
ooo0000000
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps
